Mathematisches Institutskolloquium

Das Mathematische Institutskolloquium richtet sich an ein breites mathematisches Publikum (mit Bachelor Abschluss in Mathematik). Es soll die Diskussionen über die mathematischen Spezialisierungen der verschiedenen Arbeitsgruppen am Institut fördern. Außerdem sollen auch Studierende (Master-Studierende und fortgeschrittene Bachelor-Studierende) durch das Kolloquium die Gelegenheit erhalten sich über aktuelle Themen der Mathematik zu informieren.

Wintersemester 2021/2022

  • Prof. Dr. Jan Sieber (University of Exeter, UK)
    "Delay differential equations - numerical treatment and the case of large delay"
    Abstract: Delay differential equations (DDEs), in which some of the arguments enter with a time delay, but which otherwise look like ordinary differential equations, occupy a place somewhere between ordinary differential equations and partial differential equations (PDEs) with one space dimension. This is noticeable when implementing numerical methods, especially for finding equilibria, periodic solutions and the spectra of the linear DDEs. When the delay becomes large the limiting behaviour of some periodic oscillations approaches that of patterns in PDEs. A particular example are "temporal dissipative solitions" periodic pulses caused by delayed feedback into an excitable system.
    (Joint work with Serhiy Yanchuk, Stefan Ruschel, Matthias Wolfrum)
    12.01.2022, 15:15 Uhr, Online-Veranstaltung
  • Prof. Dr. Ivan Veselić (TU Dortmund)
    "Uncertainty relations and applications"
    Abstract: Uncertainty relations or unique continuation estimates for various classes of functions are investigated in several fields of mathematical analysis. They have also a number of interesting applications, among them those in mathematical physics and the theory of partial differential equations.  While in other areas uncertainty implies less knowledge or weaker mathematical results, in these cases uncertainty principles in fact improve our knowledge about certain mathematical objects.
    The talk aims at shedding a bit of light on these aspects of uncertainty principles.
    15.12.2021, 16:00 Uhr (Time updated 09 Dec.), Online-Veranstaltung
  • Prof. Dr. Wilhelm Stannat (TU Berlin)
    "Mean-field approach to Bayesian estimation of Markovian signals"
    Abstract: Estimating Markovian signals X from noisy observations is an important problem in the natural and engineering sciences. Within the Bayesian approach the underlying mathematical problem essentially consists in the (stochastic) analysis of the conditional law of X with a view towards its efficient numerical approximation.
    In this talk I will discuss mean-field type descriptions of the conditional law of X, when X is the solution of a stochastic differential equation, and present recent results on corresponding ensemble-based numerical approximations.
    The talk is based on joint work with T. Lange, S. Pathiraja and S. Reich.
    References:
    [1] S. Pathiraja, S. Reich, W. Stannat: McKean-Vlasov SDEs in nonlinear filtering,
     SIAM J. Control Optim. 59 (2021), no. 6, 4188–4215.
    [2] S. Pathiraja, W. Stannat: Analysis of the feedback particle filter with diffusion
     map based approximation of the gain, Foundations of Data Science 3 (2021): 615-645.
    [3] T. Lange, W. Stannat: Mean field limit of Ensemble Square Root Filters - discrete
     and continuous time, Foundations of Data Science 3 (2021): 563-588.
    17.11.2021 um 15:15 Uhr, Ulmenstr. 69, Haus 3, HS 326/327 (Hybridveranstaltung) 
  • Prof. Constantinos Siettos (University of Naples Federico II, Italy)
    "Numerical Solution of Nonlinear PDEs and Stiff Problems of ODEs with Random Projection Networks and Extreme Learning Machines"
    Abstract: We use a class of machine learning the so-called Random Projections Networks and Extreme Learning Machines to numerically solve nonlinear partial differential equations (PDEs) and stiff problems of ODEs. For our demonstrations, we study several benchmark problems, namely (a) the Rober and Van-der Pol ODEs and, (b) the one-dimensional viscous Burgers and, the one- and two-dimensional Bratu PDEs. We also show how one can expolit the proposed methodology to construct bifurcation diagrams past limit points. The numerical efficiency of the proposed numerical machine learning scheme is compared against well established numerical analysis methods such as the adaptive Runge-Kutta ode45 and the ode15s a variable-step, variable-order solver based on the numerical differentiation formulas for solving the ODEs and central finite differences (FD) and Finite-element (FEM) methods for solving PDEs. We show that the proposed machine learning framework, regarding the solution of ODEs yields good numerical approximation accuracy without being affected by the stiffness, thus outperforming in same cases the ode45 and ode15s integrators, while regarding the solution of PDEs outperforms FD and importantly FEM for medium to large sized grids in terms of computational times and numerical accuracy.
    13.10.2021, 15:15 Uhr,  Online-Veranstaltung

Sommersemester 2021

  • Dr. Paolo Di Tella (University of Rostock)
    "On Martingale Representation Theorems"
    Abstract:  A central result in Stochastic Analysis is the martingale representation theorem of the Brownian motion. In this talk we are going to present classical result and extensions of the Brownian martingale representation theorem in more general contexts. We shall then present some applications to mathematical finance.
    14.07.2021, 15:15 Uhr, Online-Veranstaltung
  • Prof. Kim Knudsen (Technical University of Denmark)
    "Electromagnetic imaging – mathematical analysis and computations"
    Abstract:
    In this talk we will look at inverse problems related to electromagnetic imaging. One example is Electrical Impedance Tomography (EIT), mathematically known as the Calderón problem, where the goal is to identify a body’s interior electrical conductivity distribution from measurements of voltages and currents on the surface of the body. This problem is severely ill-posed and requires heavy regularization techniques to be implemented before allowing for image reconstruction even with low resolution and contrast.
    Recently, novel hybrid imaging methods such as Acousto-Electric Tomography and Magnetic Resonance EIT have appeared. These approaches exploit different coupled physical phenomena and therefore hold promise for much more accurate and stable methods than EIT.
    From a mathematical analysis and computational perspective we consider the three different examples; we will formulate the relevant models, pose fundamental questions and give (partial) answers.
    16.06.2021, 15:15 Uhr, Online-Veranstaltung

Sommersemester 2020

  • Prof. Dr. Bernd Sturmfels (Direktor am Max-Planck-Institut für Mathematik in den Naturwissenschaften Leipzig; Professor University of California at Berkeley)
    "3264 Conics in a Second"
    Abstract: Enumerative algebraic geometry counts the solutions to certain geometric constraints. Numerical algebraic geometry determines these solutions for any given instance. This lecture illustrates how these two fields complement each other, especially in the light of emerging new applications. We start with a gem from19th century geometry, namely the 3264 conics that are tangent to five given conics in the plane. This topic was featured in the January 2020 issue of the Notices of the American Mathematical Society.  We conclude with an application in statistics, namely maximum likelihood estimation for linear Gaussian covariance models.
    17.06.2020, 15:00 Uhr, Online-Veranstaltung
  • Prof. Dr. Bernold Fiedler (FU Berlin)
    "Good to be late, precisely"
    Abstract
    13.05.2020, 15:15 - 16:15 Uhr, Online-Veranstaltung
  • Prof. Dr. Armin Iske (Universität Hamburg)
    "Kernel-based approximation methods for data analysis and machine learning"
    Abstract
    15.04.2020, 15:00 - 16:00 Uhr, Online-Veranstaltung